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Lean-Workbook Plus 12106: Trigonometric identity

Proved
WorkbookRestored.plus_12106

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

Prove that sin⁡(a)cos⁡(a)+sin⁡(b)cos⁡(b)=sin⁡(a+b)cos⁡(a−b)\sin(a)\cos(a)+\sin(b)\cos(b)=\sin(a+b)\cos(a-b)

Source: Lean-Workbook row lean_workbook_plus_12106 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_12106 (a b : ℝ) : sin a * cos a + sin b * cos b = sin (a + b) * cos (a - b)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_12106; immutable original Prove2Me node 26551301-e44f-499f-b904-3f9c154fce03

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